Inset faces individually with thickness falloff
You could do this by converting to a curve, extruding and scaling with proportional editing, then converting back to mesh.

1) Convert to curve


2) In edit mode, select everything and set the tilt to 90°


3) Extrude the curve


4) With linear proportional editing, select a row of vertices and scale the Radius property (Alt+S)


5) Convert back to a mesh